Copernicus' complex Mercury model in De revolutionibus is virtually identical, geometrically, to Ibn al-Šāṭir's (ca. 1305 – ca. 1375). However, the model in his earlier Commentariolus is different and in many ways unworkable. This has led some to claim that the younger Copernicus did not understand his predecessor's model; others have maintained that Copernicus was working totally independently of Ibn al-Šāṭir. We argue that Copernicus did have Ibn al-Šāṭir's models but needed to modify them to conform to a “quasi-homocentricity” in the Commentariolus. This modification, and the move from a geocentric to heliocentric cosmology, was facilitated by the “heliocentric bias” of Ibn al-Šāṭir's models, in which the Earth was the actual center of mean motion, in contrast to Ptolemy and most Islamicate astronomers. We show that: 1) Ibn al-Šāṭir sought to reproduce Ptolemy's critical elongation at the trines(±120°), but changed the Ptolemaic values at 0, ±90, and 180°; 2) in the Commentariolus, Copernicus does not try to produce viable elongations for Mercury; and 3) by the time of writing De revolutionibus, Copernicus is in full control of the Mercury model and is able to faithfully reproduce Ptolemy's elongations at all critical points. We also argue that claims regarding “natural” solutions undermining transmission are belied by historical evidence.

As their greek predecessors, mathematicians and arab-speaking philosophers raised several important epistemological questions. One of those questions concerns the concept of equality and the concept of congruence of geometric magnitudes. What was the meaning of such concepts? How were they related to the idea of movement? Answers to these questions were often combining metric elements and other, philosophical (topological) elements, and I chose to study those of a mathematician, of a philosopher, and of a mathematician-philosopher.

In this paper, I examine the opposition between direct proof and proof per impossibile, introduced by al-Sijzī (second half of the 10th century) in his treatise entitled The side is not commensurable with the diagonal. From this example he gives to illustrate this opposition, al-Sijzī argues the superiority of the direct proof. In this paper, I also give the editio princeps of his treatise, as well as its first translation.

This paper shows for the first time that Maimonides significantly relied on Avicenna's “Refutation of astrology” (Al-Išāra ilā fasād ῾ilm aḥkām al-nujūm) when composing his own refutation, the “Epistle on astrology” (῾Al Gezērat ha-kōkhabīm). Maimonides consulted a copy of Avicenna's Refutation, partially using its structure as a model for his Epistle, and adapting some of its arguments. Therefore, it may be said with certainty that Maimonides carefully read at least one of Avicenna's works, and that his Epistle is not based solely on his own previous works, the “Commentary on the Mishnah”, the “Code of Jewish law”, and the “Guide of the perplexed”.

In this paper, we present the Aristotelian theory of comets, which is well known in the Muslim West through the commentaries of Ibn Rušd and Ibn Bāǧǧa. This aspect is covered three centuries later in an unknown manuscript attributed to the famous mathematician Ibn Ġāzī al-Miknāsī (1437-1513), and this text is not present in the known list of his works. The author devotes a part of his manuscript to the comet astrology following Ptolemy, and introduces a critical position of Iḫwān al-Ṣafā’, characterized by the rejection of the sidereal comets idea. We are also interested in comet classifications given by Ibn Ġāzī and another author ‘Alī al-Antākī. We found that the content of the De cometis of pseudo-Ptolemy is analogous with the text of Ibn Ġāzī, and almost identical to the text of al-Antākī. Then, we are interested in observations of comets from the 9th to the end of the 19th century in North Africa and in Islamic Spain (Andalusia), recorded in some Arabic manuscripts on astronomy and history, which have never been the subject of an extensive study. The studied observations are: the two comets X/975 P1 and X/998 D1 reported by an anonymous author of the 15th century, the X/1381 V1 comet reported by Ibn al-Qāḍī (1553-1616), the passage of Halley's comet in 1456 reported by Muḥammad al-Zarkašī (1434-1525), the C/1743 X1 comet observed by ‘Abd al-Razzāq ibn Ḥamadūš (1695-1785), which confirm its fan structure, the two observations of Ibn ‘Alī al-Šrīf al-Šalāṭī of the D/1770 L1, and especially the C/1769 P1 comet. The graphic representation of this latter comet is unprecedented in the Muslim West.

In this article, I examine key passages from the Aš῾arite theologian Faḫr al- Dīn al-Rāzī’s (d. 606/1210) final work, Al-Maṭālib al-῾āliya (“ The lofty inquiries ”), in order to theorize Rāzī’s cosmology and angelology. In his attempt to prove the existence of these beings, Rāzī divides reality into material and intelligible realms. Angels, which signify the celestial intellects and spheres, exist as non-space-occupying beings and represent an aspect of the intelligible world. Of these, some are associated with celestial bodies, and others are entirely unassociated with materiality. I then present evidence for the possibility that Rāzī believed that these celestial spiritual beings are pre-eternal with God. These positions indicate a certain degree of conceptual continuity with the falsafa tradition, and reflect al-Ġazālī’s (d. 505/1111) previous integration of the philosophical structure of reality into some of his texts. Additionally, one may look to other philosophical currents that developed in the Islamic world beyond the falāsifa, and connect Rāzī’s cosmology to both the Hermetic tradition and the Epistles of the Iḫwān al-Ṣafā᾿.

Avicenna's logic is presented in many treatises, of which the most important is Al-Qiyās (Prior analytics), which is included in his encyclopaedic book Al-Šifā’. But the treatise entitled Manṭiq al-mašriqiyyīn is said to express Avicenna's own logic by some commentators. One can thus ask: is this treatise in conflict with Al-Qiyās and the other logical writings? In this paper, we will answer this question by comparing Avicenna's analyses of the absolute – i. e. non modal – propositions. We will show that there is no radical difference between both treatises in this respect, since most conditions added to the absolute propositions in Al-Qiyās can be found in Manṭiq al-mašriqiyyīn. These conditions are: (1) “as long as S exists”, (2) “as long as it is S”, (3) “as long as it is P”, (4) “at some times”, (5) “at one determined time”, (6) “sometimes but not permanently”. In Manṭiq al-mašriqiyyīn, the ḍarūrīya contains (1), the lāzima contains (2), the muntašira contains (4), the mafrūḍa contains (5), the wujūdiyya contains (6), but (3) is abandoned. The waqtiyya was evoked in Al-Qiyās, although not classified. So the temporal analysis initiated in Al-Qiyās is pursued and developed in Manṭiq al-mašriqiyyīn, even if in the latter it is sometimes confused.

This paper argues that Ibn Ṭufayl (d. 1185) in his Ḥayy ibn Yaqẓān offers a surprisingly intellectual reading of the term fiṭra (pl. fiṭar) and one that has significant consequences for our understanding of the story. We will see that at crucial junctures in the text, fiṭra emerges solely in an intellectual context, implying a gulf amongst humanity that defies common understandings of the term as egalitarian. This gulf, I argue, illuminates the political implications of the tale. For while he emphasizes the broad compatibility of the more established, revealed and the philosophical path recently arrived in Andalusia, Ibn Ṭufayl, with the help of fiṭra, shows that the philosophical life is one for the very few. Attention to Ibn Ṭufayl's use of fiṭra might thus explain one of his reasons for writing this tale for the court. Its overall message heightens the role of religion and tempers the political significance of philosophy in two ways: by arguing that only select individuals have the capacity to access truth independently from revelation; and by denying these exceptionally gifted the ability to communicate their findings to the masses.

In several places and for different purposes, Ibn al-Haytham has studied the variations of a well-known function. The context of these applications reveals some characteristics of Ibn al-Haytham's mathematical and physical thought. An in-depth study of his mathematical proofs of monotony show how close he was from an elaborate concept of the continuous.

Ibn Raḥīq is an 11th century scholar who compiled a book on popular astronomy. This work included a section in which he summarizes basic knowledge of the Milky Way as it was wide spread in the first centuries after the hejira. Ibn Raḥīq gives a comprehensive overview of the perception of the Milky Way that reaches from its use as a test for knowledge of the religious tradition and for agricultural purposes on the one hand to an exact astronomical description of its shape in the sky during the year and to theories of its nature and composition on the other hand. We use a comparison of his text to those of Ibn al-Haytham and others to investigate the role the Milky Way played in early Islamic civilization from its beginning until the 15th century.

Before Ṯābit b. Qurra's translation, there was a first Arabic version of Nicomachus’ Introduction to arithmetic. Full of mistakes, it was revised by an anonymous student of al-Kindī. Thanks to the part that Freudenthal and Levy have edited and translated, we are now able to identify this reviser as Aḥmad b. al-Ṭayyib al-Saraḫsī, who we also identified as the author of the Rasā᾿il Iḫwān al-Ṣafā᾿. The comparison of the gloss written by this reviser with a new fragment of Saraḫsī on one part, and with the “ Epistles of the Brethren in Purity ” on the other, corroborate Saraḫsī’s authorship of the epistles. Furthermore, studying the misunderstandings on Nicomachus’ text in this kindianised version gives a new light on al-Kindī’s attempt to unify philosophy and on the specific ontology of the Brethren in Purity.